Two objects that are moving along an $x y$ -plane on a frictionless floor collide. Assume that they form a closed. isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. What are the missing values $\left(a, b\right)?$

	Before collision		After collision
Object	$p_X$	$p_Y$	$p_X$	$p_Y$
A	$-4$	$5$	$3$	$a$
B	$b$	$-2$	$4$	$2$

 

Figure shows a hollow cube of side ' $\mathrm{a}$ ' and volume ' $\mathrm{V}.$ There is a small chamber of volume $\mathrm{V}/4$ in the cube as shown. The chamber is completely filled by $\mathrm{m} \mathrm{kg}$ of water. Water leaks through a hole $\mathrm{H}$ and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is

A block 'A' of mass $\mathrm{m},$ hits horizontally the rear side of a spring (ideal) attached to a block $B$ of mass $m_2$ resting on a smooth horizontal surface. After hitting, ' $A$ ' gets attached to the spring.

Some statements are given at any moment of time:
i. If velocity of $A$ is greater than $B,$ then kinetic energy of the system will be decreasing.
ii. If velocity of $A$ is greater than $B,$ then kinetic energy of the system will be increasing.
¡ii. If velocity of $A$ is greater than $B,$ then momentum of the system will be decreasing. iv. If velocity of $A$ is greater than $B,$ then momentum of the system will be increasing.
Now select correct alternative:

Two blocks of masses $\mathrm{m}$ and $4 \mathrm{m}$ lie on a smooth horizontal surface connected with a spring in its natural length. Mass $\mathrm{m}$ is given velocity $v_0$ through an impulse as shown in figure. Which of the following is not true about subsequent motion?

Two identical blocks, having mass $\mathrm{M}$ each, are conjugated and placed on a smooth floor as shown in figure. A small block of mass $\mathrm{m}$ is released from position as shown. Velocity of block $\mathrm{B}$ is maximum

In figure, a hollow tube of mass $\mathrm{M}$ is free in horizontal direction. The system is released from rest. There is no friction present. The tube and blocks are taken as system.

i. Momentum of the system is conserved in $\mathrm{x}$ -direction.
ii. Speed of $\mathrm{A}$ w.r.t. $\mathrm{M}=$ Speed of $\mathrm{B}$ w.r.t. $\mathrm{M}$

¡ii. Trajectory of centre of mass is $\mathrm{X}$ -constant. iv. Centre of mass has finite acceleration.
Evaluate the above statements and choose the correct option from the following: